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The Laplace operator detects edges
between constant amplitude volumes
(Figure 18).
Applied to the synthetic test case,
the Laplace operator delineates the discontinuity
but only partially suppresses the plane waves
(Figure 20).
The wavelet along the discontinuity changes its polarity
depending on the contrast of the adjacent plane waves.
The somewhat lower amplitude of the Laplace operator
among the horizontal plane wave is probably due to
the exact zero of the horizontal component.
zeroFoltLap
Figure 20
Laplace operator applied to synthetic test case.
The Laplace operator slightly enhances the fault plane
between the neighboring planewave volumes.
However,
the planewave oscillations lead to noticeable residuals in the
planewave volumes.

 
Applied to the first seismic test case
(Figure 21),
the Laplace operator creates a discontinuity map
that generally resembles the original seismic image.
The wavefieldlike character of the time slice remains.
The fault marked R in the original image 8
is not enhanced:
neither are any other faults.
Applied to the image of the North Sea horst,
the Laplace operator yields
a similarly disappointing discontinuity map (not shown).
gulfFoltTotLap
Figure 21
Laplace operator applied to salt image.
The Laplace operator does not change the character of the
original seismic image. In particular, the discontinuity
map fails to delineate the sought faults.
Next: Horizontal correlation
Up: Laplace operator
Previous: Laplace operator
Stanford Exploration Project
3/8/1999